Theoretically, yes. Functionally, no. When you go to pay for something with your infinite bills, would you rather pay with N number of 100 dollar bills or get your wheelbarrow to pay with 100N one dollar bills? The pile may be infinite, but your ability to access it is finite. Ergo, the “denser” pile is worth more.
Yeah, this is what it comes down to. In calculus, infinity doesn’t exist, you just approach it when you take the limit. You’ll approach it “quicker” with the 100 dollar bills, so to speak
You’re thinking of a different calculus problem in this case we are comparing the growth rate of 100*infty vs infty. In calculus, you cannot accelerate the growth of \infty. If you put infty / infty your answer will be undefined (you can double check with Wolfram), similarly, if you put 100*infty / infty, you will also get undefined
If we’re adding real world hypotheticals you would be paying for your shit on card anyway. You just go to the bank with how ever many truck loads of $100 bills when ever you needed a top up. Secondly you wouldn’t be doing it yourself, you pay someone else to do it. Thirdly as soon as the government found out you effectively had a money printer they would put you in prison or disappear you to prevent you from collapsing their money system, not to mention the serial numbers on the notes would have to be fraudulent because they wouldn’t match up with mints. And finally any physical object with an infinite quantity would be the size of the universe, likely causing either black hole or destroying the universe and us along with it. So in closing what sounds like a great situation is probably worth any potential risk
To establish whether one set is of a larger cardinality, we try to establish a one-to-one correspondence between the members of the set.
For example, I have a very large dinner party and I don’t want to count up all the forks and spoons that I’ll need for the guests. So, instead of counting, everytime I place a fork on the table I also place a spoon. If I can match the two, they must be an equal number (whatever that number is).
So let’s start with one $1 bill. We’ll match it with one $100 bill. Let’s add a second $1 bill and match it with another $100 bill. Ad infinitum. For each $1 bill there is a corresponding $100 bill. So there is the same number of bills (the two infinite sets have the same cardinality).
You likely can see the point I’m making now; there are just as many $1 bills as there are $100 bills, but each $100 bill is worth more.
You’re right that we don’t need to, but mathematicians can use this method to prove that two infinite sets are the same size. This is how we know that the infinite set of whole numbers is the same size as the infinite set of integers. We can also prove that the set of real numbers is larger than the set of whole numbers.
I’m not quite sure how else to explain it, so I’ll link a Numberphile video where they do the demonstration on paper: www.youtube.com/watch?v=elvOZm0d4H0&t=19s . Here you can see why it’s useful to try to establish this 1-1 correspondence. If you can’t do so, then the size of the two infinite sets are not equal.
But the creation of each additional bill devalues the currency. At some point the value of all this paper money is negative because it’s not worth keeping and storing. The point at which they cross from positive to negative value would give them zero value, and they’d be equal.
You likely can see the point I’m making now; there are just as many $1 bills as there are $100 bills, but each $100 bill is worth more.
But the monetary value of the bills in each stack still adds up to infinity for both. It’s like having an uncapped Internet connection at 56 KBit/s versus 100 MBit/s: You can download all the things with both, but that alone doesn’t make them equal.
I think you’re misunderstanding the math a bit here. Let me give an example.
If you took a list of all the natural numbers, and a list off all multiples of 100, then you’ll find they have a 1 to 1 correspondence.
Now you might think “Ok, that means if we add up all the multiples of 100, we’ll have a bigger infinity than if we add up all the natural numbers. See, because when we add 1 for natural numbers, we add 100 in the list of multiples of 100. The same goes for 2 and 200, 3 and 300, and so on.”
But then you’ll notice a problem. The list of natural numbers already contains every multiple of 100 within it. Therefore, the list of natural numbers should be bigger because you’re adding more numbers. So now paradoxically, both sets seem like they should be bigger than the other.
The only resolution to this paradox is that both sets are exactly equal. I’m not smart enough to give a full mathematical proof of that, but hopefully that at least clears it up a bit.
Adding up 100 dollar bills infinitely and adding up 1 dollar bills infinitely is functionally exactly the same as adding up the natural numbers and all the multiples of 100.
The only way to have a larger infinity that I know of us to be uncountably infinite, because it is impossible to have a 1 to 1 correspondence of a countably infinite set, and an uncountably infinite set.
~~I was thinking that, bill for bill, the $100 bill will always be greater value. But I can see the plausibility in your argument that, when we’re counting both the value of the members of each set, the value of the $100 bill pile can always be found somewhere in the series of $1 bills. The latter will always “catch up” so to speak. But, if this line of reasoning is true, it should apply to other countably infinite sets as well. Consider the following two examples.
First, the number of rational numbers between 0 and 1 is countably infinite. That is, we can establish a 1-1 correspondence between the infinite set of fractions between 0-1 and the infinite set of positive integers. So the number of numbers is the same. But clearly, if we add up all the infinite fractions between 0 and 1, they would add up to 1. Whereas, adding up the set of positive integers will get us infinity.
Second, there are equally many positive integers as there are negative integers. There is a 1-1 correspondence such that the number of numbers is the same. However, if we add up the positive integers we get positive infinity and if we add up all the negative integers we get negative infinity. Clearly, the positive is quantitatively greater than the negative.
In these two cases, we see that a distinction needs to be made between the infinite number of members in the set and the value of each member. The same arguably applies in the case of the dollar bills.~~
Ah but you see if you take into consideration it’s talking about bills and not money in an account you have to take into consideration the material reality. A person who receives more 100s would have an easier time depositing and spending the money therefore they have higher utility, therefore they are worth more than the 1s.
Sure they may have the same amount of numbers (and 1, 2,3… May even be larger because you’ll eventually repeat in the 1:1 examile) but in reality the one with the 100s will have an easier time using their objects (100 dollar bills) than the ones who pick the 1 dollar bills
Infinity is a concept that can’t be reached so it can’t be counted up fully. Its not a hard number so you can’t get a full value from it since there is always another number to reach. Therefore you only peak at ∞ in any individual moment. You can never actually count it.
If you’re responding to the part about countable infinity and uncountable infinity, it’s a bit of a misnomer, but it is the proper term.
Countably infinite is when you can pick any number in the set and know what comes next.
Uncountably infinite is when it’s physically impossible to do that, such as with a set of all irrational numbers. You can pick any number you want, but it’s impossible to count what came before or after it because you could just make the decimal even more precise, infinitely.
The bizarre thing about this property is that even if you paired every number in a uncountably infinite set (such as a set of all irrational numbers) with a countably infinite set (such as a set of all natural numbers) then no matter how you paired them, you would always find a number from the uncountably infinite set you forgot. Infinitely many in fact.
It’s often demonstrated by drawing up a chart of all rational numbers, and pairing each with an irrational number. Even if you did it perfectly, you could change the first digit of the irrational number paired with one, change the second digit of the irrational number paired with two, and so on. Once you were done, you’d put all the new digits together in order, and now you have a new number that appears nowhere on your infinite list.
It’ll be at least one digit off from every single number you have, because you just went through and changed those digits.
Because of that property, uncountably infinite sets are often said to be larger than countably infinite sets. I suppose depending on your definition that’s true, but I think of it as just a different type of infinity.
Sure if you’re talking about a concept like money, but we’re talking about dollar bills and 100 dollar bills, physical objects. And if you’re talking about physical objects you have to consider material reality, if you’re choosing one or the other the 100 dollar bills are more convinient. Therefore they have more utility, which makes them have a higher value.
What is worth? Would you rather have 500 1s or 5 100s? You already said you’d take the 100s, why? I would take the 100s because I personally value the convenience of 100s more than the 1s, so to me, a single 100 is worth more than 100 1s. Worth doesn’t need to imply the monetary value of the money.
The convenience/utility makes the 100s worth more even if they’re both valued the same
Don’t care. They both get deposited at my bank the same.
You already said you’d take the 100s, why?
An acknowledgement to the point you were making that was a digression from the discussion at hand. My mistake apparently.
I would take the 100s because I personally value the convenience of 100s more than the 1s, so to me, a single 100 is worth more than 100 1s.
I personally would not accept a Genie wish for either as the mass would create a black hole that would destroy the universe. There is no “practical consideration” when dealing with infinities. Knowing how to work with infinities is useful for complex mathematics, but there is no real world application until you simplify away the infinities.
Worth doesn’t need to imply the monetary value of the money.
It very much does imply the monetary value of the money. It can mean other things if you want to define it as such, but you need to before hand in such a case. It was not defined differently by OP.
I see I made a mistake by acknowledging your argument, and trying to indicate my understanding there of, before trying to get back to the point at hand that an infinite number of $1 bills is worth the same amount as an infinite number of $100 bills.
I was actually discussing this with my wife earlier and her position is that the 1 dollar bills are better because it’s tough to find somebody who’ll split a 100, and 100s don’t work in vending machines.
I thought the hundreds would be better because you could just deposit them in the bank and use your card, and banks often have limits on how many individual bills you can deposit at once, so hundreds are way better for that.
You’re right that they’re the same size but you’re mistaken when you try to assign a total value to the stack. Consider breaking each $100 bill into 100 $1 bills. The value is the same, clearly. So for each pair, you have a $1 bill and a small stack of 100 $1 bills. Now combine all singles back together in an infinite stack. Then combine all stacks of 100 into an infinite stack.
And you know what? Both infinite stacks are identical. They have the same value.
You could make an argument that infinite $100 bills are more valuable for their ease of use or convenience, but infinite $100 bills and infinite $1 bills are equivalent amounts of money. Don’t think of infinity as a number, it isn’t one, it’s infinity. You can map 1000 one dollar bills to every single 100 dollar bill and never run out, even in the limit, and therefore conclude (equally incorrectly) that the infinite $1 bills are worth more, because infinity isn’t a number. Uncountable infinities are bigger than countable ones, but every countable infinity is the same.
Another thing that seems unintuitive but might make the concept in general make more sense is that you cannot add or do any other arithmetic on infinity. Infinity + infinity =/= 2(infinity). It’s just infinity. 10 stacks of infinite bills are equivalent to one stack of infinite bills. You could add them all together; you don’t have any more than the original stack. You could divide each stack by any number, and you still have infinity in each divided stack. Infinity is not a number, you cannot do arithmetic on it.
100 stacks of infinite $1 bills are not more than one stack of infinite $1 bills, so neither is infinite $100 bills.
You can map 1000 one dollar bills to every single 100 dollar bill and never run out, even in the limit, and therefore conclude (equally incorrectly) that the infinite $1 bills are worth more, because infinity isn’t a number.
Yes, the mapping that you’re describing isn’t useful; but that doesn’t invalidate the simple test that we can do to prove that two infinite sets are the same. And the test is pretty intuitive in some cases. If for every fork there is a spoon, then they must be an equal number. And if for every positive whole number (e.g “2”) there is a negative whole number (e.g. “-2”), then the set of positive whole numbers and the set of negative whole numbers must be the same.
Another thing that seems unintuitive but might make the concept in general make more sense is that you cannot add or do any other arithmetic on infinity.
I agree with you that adding infinity to itself just gets you the same number. But now we’re starting to ask: just what is infinity? We could think of infinity as a collection of things or we could think of infinity like we do numbers (yes, I know infinity is not technically among the real numbers). In the latter sense we could have a negative infinity {-1…-2…-3…etc.} that is quantitatively “worth less” than a countable positive infinity. On the other hand, if we think of infinity as a collection of stuff, then you couldn’t have a negative infinity because you can’t have less than zero members in the set.
I’ll admit that I’m getting out of my depth here since I know this stuff from philosophical study rather than maths proper. As with anything, I’m happy to be proven wrong, but I’m quite sure about the 1-1 correspondence bit.
Your 1-1 relationship makes sense intuitively with a finite set but it breaks down with the mathematical concept of infinity. Here’s a good article explaining it, but DreamButt’s point of every set of countable infinite sets are equal holds true because you can map them. Take a set of all positive integers and a set of all positive, even integers. At first glance it seems like the second set is half as big right? But you can map them like this:
Set 1 | Set 2
1|2
2|4
3|6
4|8
5|10
6|12
If you added the numbers up on the two sets you would get 21 and 42 respectively. Set 2 isn’t bigger, the numbers just increased twice as fast because we had half as many to count. When you continue the series infinitely they’re the same size. The same applies for $1 vs $100 bills.
$1|$100
$2|$200
$3|$300
In this case the $1 bills are every integer while the $100 bills is the set of all 100’s instead of all even integers, but the same rule applies. Set two is increasing 100x faster but that’s because they’re skipping all the numbers in between.
I understand that both sets are equally infinite (same cardinality). And I do see the plausibility in your argument that, in each case, since there’s an infinite number of bills their value should be equally infinite. If your argument is correct, then I should revise my understanding of infinity. So maybe you can help me make sense of the following two examples.
First, the number of rational numbers between 0 and 1 is countably infinite. That is, we can establish a 1-1 correspondence between the infinite set of fractions between 0-1 and the infinite set of positive integers. So the number of numbers is the same. But clearly, if we add up all the infinite fractions between 0 and 1, they would add up to 1. Whereas, adding up the set of positive integers will get us infinity.
Second, there are equally many positive integers as there are negative integers. If we add up the positive integers we get positive infinity and if we add up all the negative integers we get negative infinity. Clearly, the positive is greater than the negative.
In these two cases, we see that a distinction needs to be made between the infinite number of members in the set and the value of each member. The same arguably applies in the case of the dollar bills.
But clearly, if we add up all the infinite fractions between 0 and 1, they would add up to 1.
0.9 and 0.8 are in that set, so they would add up to at least 1.7. In fact if you give me any positive number I can give you a (finite!) set of (distinct) fractions less than 1 which sum to more than that number. In other words, the sum is infinite.
I meant to say that we can infinitely divide the numbers between 0 and 1 and then match each with an integer. But I realized that the former wouldn’t be rational numbers, they would be real numbers.
That aside, I see now that the original idea behind the meme was mistaken.
I meant to say that we can infinitely divide the numbers between 0 and 1 and then match each with an integer. But I realized that the former wouldn’t be rational numbers, they would be real numbers.
That aside, I see now that the original idea behind the meme was mistaken.
My scanner defaults to .tiff for some reason if I scan from the button and it cannot be changed. Have to scan from gnome-document-scanner if I want different formats.
Back in the 90s, I was asked to critique a local business web site. I noticed a picture wasn’t loading correctly on Netscape Navigator when it was working fine on IE. Turned out, the designer had stuck in a 5MB BMP image. This when a whole lot of people were still on 56K modems.
Yeah it pretty much feels like a miracle. I’m down 55lbs in 6 months, ends up at like 2-3lbs per week which is considered a healthy loss. I’ve done literally nothing different with eating, I just… eat less.
It was slow for me. I was on .25mg/week of Ozempic at the start and now am on 1mg/week. It is the right amount for me. I’ve been losing 8-10lbs each month and doing nothing else but eat less. If I were to incorporate more exercise, I could lose it at a higher rate.
There’s also the bow shock you experience as your habits change. When I started, I still had the bad habit of overeating, but Ozempic won’t allow it. I eventually learned to eat less or regret it. How long have you been on it and how much have you lost so far?
Not on it, but Primary Care clinical staff. Lots of people feel underwhelmed at the start. Some are more “slow and steady” than others. I would try not to judge the clinical results until after some time at 2.4mg.
Thanks very much for this reply. I’ve been seeing a dietician whose advise is that I’ve been eating too little to lose weight and that feels absolutely stupid.
I’ll admit since I increased my intake I’ve been feeling better, and I haven’t gained any weight, but I’m impatient. I wish I could just stop eating and lose it that way…
I’m down 65 lbs! Ozempic/semaglutide has muzzled my out of control eating. I’ve been on different weight loss meds and none have targeted the cause: bored eating when I’m not hungry. I still eat pretty much whatever I want, but I can’t handle any overeating. I made it through the holidays and didn’t gain any weight! I enjoyed the holiday goodies and was good to have a small amount. Going back for seconds sort of disgusts me. Went to the doctor today and my A1C is 5.8! It’s not been that low in 15 years!
I was on sumaglutide for a month. Made me ravenously hungry and gave me nonstop stomach cramps that only went away when eating. Fuckin’ sucked, as it raised my fasting blood sugar by a lot, too.
I was on Ozempic for about two years due to Type 2 and a bad A1C. I lost about 10lbs but gained it back as soon as I switched medication. Everyone is praising these drugs as miracles, and they are… But only if you’re able to keep the habit they help you build. I’m now on Mounjaro, and I tried Trulicity. Both have done better good for me than Ozempic ever did. My A1C is almost normal, and my energy is so much better. I’ve also lost about 10lbs and am exercising more/eating less and building the good habits. It definitely changes your metabolism, and makes you feel fuller faster. So it can be a huge blessing if you need it.
In my experience, it doesn’t matter what you set your age or distance range to in Tinder, because you’re going to get people 10 years older or younger and a hundred miles farther away than you specify anyway.
Yeah, that just never seems to work for long. I currently have it set to 35-45, and it’s showing me 20-somethings. And I live in a huge city, so it’s not like it’s running out of people in my age range to show me.
I’m super confused. It seems most of this conversation misses the meme format. Everyone is agreeing with the middle guy. That’s how the meme works. The middle guy is right, but that’s not the point. It’s like I’m taking crazy pills.
While I wish I didn’t just learn this meme’s far-right origins, I have to disagree with you. The middle guy is supposed to give a correct and boring answer. The left guy is supposed to give a common and wrong answer, and the guy on the right is supposed to have an enlightened view of the wrong guy’s answer. The best example I’ve seen is the one:
[wrong] Frankenstein is the monster.
[average] No, Frankenstein is the doctor.
[enlightened] Frankenstein is the monster.
It’s still wrong to say Frankenstein was the monster. It’s deliberately misleading. So yeah, the money is the same amount, but I’d rather have a secret endless stash of hundreds than singles.
[wrong] police can get away with any crimes they want (child POV)
[average] police can’t break the law even though they are police (the way it ‘should be’)
[enlightened] police can get away with any crimes they want (reality)
The middle person thinks they are smarter than the left person. But it turns out the left person was naive but correct, as shown by the right/enlightened person having the same conclusion. IMO anyway.
EDIT: also, the point of the example you gave is that Frankenstein the Doctor IS the monster (metaphorically) because he created the actual monster - I think you have misinterpreted it.
If you take the average interpretation of “police can’t …” to mean “it’s illegal for the police to …”, then yes, the average guy is right in a boring (and tautological) way. I don’t think that’s an unreasonable way for the average person to interpret the [average] line. The meme hopes to get you thinking about the last line.
Now this money example is particularly hard to argue since if you have the interpretation that the dollar will collapse, or if you think you have to store this money, then, all resolutions suck.
If a genie were to say to me, “Anytime you need money, you can reach in your pocket and pull out a bill. Would you like it to always be $1 or always be $100?”, I think I would agree with the enlightened guy here, even though I know the boring answer is right.
I confused though. You seem to think I didn’t quite get the format, but I feel I’ve explained how I see it, and don’t see any contrast with the meme you posted. So far that’s three in the format as I understand it.
So, if your answer to the genie question I asked a bit ago is “$100s please”, then the meme would speak to you. If you truly don’t care, the guy on right is wrong in your book. I’m in the “$100s please” camp.
Dr. Frankenstein is not a monster for creating an actual monster. He is a monster for abandoning his creation and escaping the responsibility of care for his creation.
I thought we were having a friendly chat, but you really insulted my intelligence there. Do you think I would have found that meme remotely interesting if I thought Frankenstein had terminals on his neck?
Sorry, I didn’t mean to insult your intelligence in any way. Just trying to have a friendly chat also. Sometimes tone can come across wrong in text. My bad
FOR REAL lmao. These guys are so freaking gross. Anyone more than 6 years younger looks like they have baby face, no thanks, its so creepy at that point.
Uhm wat dis? If you think that gen Z people are more racist than the previous generations, then you have probably met with the minority. I rarely know a gen Z racist fella (I’m gen Z too). Tiktok could be true, but my friends definitely don’t use Tiktok and millenials use that trash site just as much as us, or maybe even the boomers too idunno.
If you grow up in the US, it’s pretty hard not to be racist because the entire culture and history is steeped in racism.
It’s taken willful self-reflection to recognize some things I say or do that are implicitly racist. If we just went about chanting, “I’m not racist,” we’d never be able to grow and improve.
On my surface go 2 I get a better experience in terms of battery life etc than with edge than the others (I’ve experimented with chrome and Firefox). So I just use edge on everything for the sync stuff. Sure has a ton of “helpful” stuff in it I have to hide it turn off though.
Huh? Wasn’t this always how this template looked like? I found it by ducking (is that what we call it?) “elmo cocaine meme template”, meanwhile “coockie monster cocaine meme template” returns nothing relevant…
EDIT: Are you making a joke about cookies that I am too dumb to understand?
I think it’s because the chrome and chromium icons are circles, like cookies. You also put a “bite mark” in the chrome icon, as if bit off like a cookie.
Oh haha no worries. I myself have never watched a ful episode of whatever show these characters are from (Sesame street? was that what it was called?) so I thought you were referencing some lore I didn’t know haha
This is wrong. Having an infinite amount of something is like dividing by zero - you can’t. What you can have is something approach an infinite amount, and when it does, you can compare the rate of approach to infinity, which is what matters.
I was just over here thinking this was about the practical utility of a $100 bill versus a wad of 100 $1 bills making an infinite quantity of the former preferable in comparison to (i.e. “worth more than”) the latter…
Imagine being the guy with an infinite money glitch but having to pay for EVERYTHING in one dollar bills. Buying even a modest sedan would be a pain in the ass. “What do you do for a living?” “I’m 47 strippers.”
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